Math: Showing how Marin's early Deathcap Rumble is flawed
At the ongoing MSI event, star SKT toplaner Marin has played Rumble twice in three games thus far. In both games, he built a surprisingly early Rabadon's Deathcap because of the lead he had accrued. However, as it turns out, Rabadon's on Rumble is actually largely inferior to Void Staff at the point in the game at which Marin was buying it. Though he played incredibly impressively in both games, I wanted to hash out why you might want to think twice before following his lead in your own soloqueue or competitive match.
At level 11 with rank 2 ultimate, rank 5 flamespitter, and rank 2 electroharpoon, Rumble's total base damage is 1430. His total AP scaling is 330%, not including things like Luden's Echo, Lichbane, or his Overheated/Danger Zone mechanic. Note that Void Staff scales with ability ranks but Rabadon's does not, so being above level 11 (as the Rumble usually will be by the time he makes this choice) only plays in favour of the Void Staff. Rabadon's instead only scales up with more AP items.
1430/330 = 433.33... AP required for scalings to equal base damage (point at which damage damage from Rabcap exceeds damage from Void Staff).
Because % magic penetration applies first, we'll test this on the target it will be not very effective against: a carry with 50 magic resist.
(100 + 50)/(100 + (50*0.65)
The passive of the Void Staff results in you dealing 13% more damage against a 50 MR target. Considering that the Rumble is probably running some magic pen in his runes or masteries, and will get 30 from Haunting Guise and Sorc Shoes, the effective MR of a 50 MR carry vs. a Void Staff Rumble should be 0. This means that Rumble's full combo will deal a full 1430 base magic damage to the target plus, with 280 AP, 924 magic damage in scalings. This totals to 2354 damage.
Assuming Marin's pre-Cap/Staff AP is about 210 as with in his game vs. EDG, Rabadon's will bring him to about 430 AP. Against the 50 MR target, if we say he penetrates 35 MR sans Void Staff, his damage will be reduced by 15/115 = 0.13 or 13%. This means his full burst combo will deal 430*3.3 + 1430 = 1419 + 1430 = 2849 damage before that reduction, but 2849 * 0.87 = 2479 full damage.
One factor in favour of Rabadon's here is the value it has for his shield, giving it about 60 bonus points of damage absorption that the Void Staff would not give.
Let's look at the comparative damage vs. targets of varying MR.
37 MR target (raw carry, no defensive items, no auras)
With Void: 2354 damage
With Rabcap: 2792 damage
IN THE LOW 60s THE TOTAL DAMAGE OF VOID STAFF OUTSTRIPS THAT OF RABADON'S DEATHCAP
75 MR target (bruiser w/ Maw, Merc Treads, maybe runes/masteries)
With Void: 2071
With Rabcap: 2037
125 MR target (tankiest mofo on the field when you're buying these items)
With Void: 1612
With Rabcap: 1495
Overall these damage comparisons favour Rabadon's. This advantage is by a significant margin from 40 MR down but above that it quickly equalizes, remaining close until the target is well over 100 MR. So, these are advantages of Rabadon's: higher damage vs. those with less than 60MR, significantly higher damage vs. those with less than 40 MR, slightly better for Scrap Shield. Void Staff has a few advantages of its own: higher damage vs. targets with over 60 MR, significantly higher damage vs targets with 120 MR, and significantly less reliance on Electro-Harpoon (and to a lesser extent Flamespitter) for damage, making it synergize better with Zhonya's as well as the tank wall meta.
However, Void Staff also wields an advantage we haven't yet considered: price. One of InvertedComposer's most vaunted metrics for comparing items is Damage Per Cost Adjustment (DPCA). With the DPCA multiplier being 0.695 for the RabCap, we can go through and consider again our stats at each point. This section was edited because it was previously completely flawed. It now considers damage versus neither item rather than including base damage fully, which heavily favoured Void Staff.
37 MR DPCA'd
Void Staff: 273
50 MR DPCA'd:
Void Staff: 783
75 MR DPCA'd:
Void Staff: 861
125 MR DPCA'd:
Void Staff: 678
As you can see, with price adjustments in place the Void Staff easily outdamages Rabadon's Deathcap in terms of damage per cost at the MR levels which will have been reached by all enemies except maybe the AD carry. In exchange, the only real advantage the Deathcap will give is a small boost to Scrap Shield and a decent damage boost against one or two squishy enemy team members. For this reason, it is usually a better decision to build Void Staff before Deathcap on Rumble.
The formulas and basis for this article were found at the site of LoL mathematics mastermind InvertedComposer. You can read more of his work here.